If $4\le x\le 8$ and $2\le y\le 7$, then what is the ratio of maximum value of (x + y) to minimum value of (x – y)?

The correct option is None of the above.

To find the required ratio, we need to calculate the maximum value of $(x+y)$ and the minimum value of $(x-y)$ based on the given ranges:

$4\le x\le 8$

$2\le y\le 7$

Step 1: Find the maximum value of $(x+y)$
To maximize the sum of two positive variables, we choose the maximum possible value for both $x$ and $y$:

Maximum value of $x=8$

Maximum value of $y=7$

$\text{Maximum value of}(x+y)=8+7=15$

Step 2: Find the minimum value of $(x-y)$
To minimize the difference $(x-y)$, we must choose the smallest possible value of $x$ and subtract the largest possible value of $y$:

Minimum value of $x=4$

Maximum value of $y=7$

$\text{Minimum value of}(x-y)=4-7=-3$

Step 3: Calculate the ratio
Now, we find the ratio of the maximum value of $(x+y)$ to the minimum value of $(x-y)$:

$\text{Ratio}=\frac{15}{-3}=-5$

Since the calculated ratio $-5$ is not present among the given choices (6, $\frac{15}{2}$, or $-\frac{15}{2}$), the correct choice is None of the above.